How to replace For loops?

I wrote an code with a lots of For loops. I want to replace them and to use functions instead.

wich functions do the same actions?

The code:

w0=(2*pi)/2001;       
ak1=zeros(1,2001);  %initializing the coeffecients array
%calculating Fourier coeffecients
for k=0:1:2000
   s=0;
   for n1= 1:1:2001
       s=a(n1)*exp(-1i*k*w0*(n1-1001))+s; 
   end
   ak1(k+1)=(1/N)*real(s);
end

Thank's for helping ,

Liron

[dpb]

Try vectorize on your expressions as starter...

Then just replace the loops with a vector expression for the variable that is in the loop...

[Liron Sabatani]

thank you very much about your answer!

I tried to vectorize but I don't succeed to get rid from all the for loops..

That's what I did:

for k=0:1:2000

n1= (1:1:2001);

s=sum(a(n1).*exp(-1i*k*w0*(n1-1001)));

ak1(k+1)=(1/N)*real(s);

end

Answer 1

[Ameer Hamza]

No functions are needed to replace the for loop in your current code. Just matrix operations are enough.

rng(0);
w0=(2*pi)/2001;       
a = rand(1,2001); % missing from your posted code
N = 2001;
n1= 1:1:2001;
k=(0:1:2000)';

s = a*exp(-1i*k*w0*(n1-1001)).';
ak1=(1/N)*real(s);

Test if the output is correct

% your code
rng(0);
w0=(2*pi)/2001;       
ak1=zeros(1,2001);  %initializing the coeffecients array
a = rand(1,2001); % missing from your posted code
N = 2001;

%calculating Fourier coeffecients
for k=0:1:2000
   s=0;
   for n1= 1:1:2001
       s=a(n1)*exp(-1i*k*w0*(n1-1001))+s; 
   end
   ak1(k+1)=(1/N)*real(s);
end

% my code
s = a*exp(-1i*k*w0*(n1-1001)).';
ak2=(1/N)*real(s); % variable name changed to ak2 for comparison

Result:

>> isequal(ak1,ak2)
ans =
  logical
   1

[Liron Sabatani]

You helped a lot me thank you!!!

[Ameer Hamza]

Glad to be of help.

[Liron Sabatani]

I tried to do the same with another part of the code but I don't succeed to do so .. please if you can help:)

k=0:1:2000;
ck(k+1)=ak1(k+1).*(1-exp(-1i.*k*w0)); %calculating ck Fourier coeffecients 

c=zeros(1,2001);  %initializing the array
for n3=1:1:2001   %calculating c signal
    k=0:1:2000;
    s4=sum(ck(k+1).*exp(1i.*k*w0*(n3-1001)));
    c(n3)=real(s4);
end

I really appreciate the help:)

[Ameer Hamza]

Following code vectorize it

rng(0);
w0=(2*pi)/2001;       
a = rand(1,2001); % missing from your posted code
N = 2001;
n1= 1:1:2001;
k=(0:1:2000)';
s = a*exp(-1i*k*w0*(n1-1001)).';
ak1=(1/N)*real(s);

k=0:1:2000;
ck=ak1.*(1-exp(-1i.*k*w0)); %calculating ck Fourier coeffecients 

n3=(1:1:2001)';
k=(0:1:2000);
s4=ck*exp(1i.*w0*(n3-1001)*k).';
c(n3)=real(s4);

[Liron Sabatani]

again thank you!! I got the way to do this:)

Answer 2

[David Hill]

No loops except arrayfun loop.

w0=(2*pi)/2001;       
n1=1:2001;
k=0:2000;
s=arrayfun(@(x)sum(a(n1).*exp(-1i*x*w0.*(n1-1001))),k); 
ak1=real(s)/N;

[Liron Sabatani]

Thank you very much!!!